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anastassius [24]
2 years ago
8

5

Mathematics
1 answer:
evablogger [386]2 years ago
5 0

Answer:

6

Step-by-step explanation:

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I found a place that will give me a 20 % discount if i spend over $50
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Work:

75 x 0.20 (20%) = 15

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3 years ago
Suppose after 2500 years an initial amount of 1000 grams of a radioactive substance has decayed to 75 grams. What is the half-li
krok68 [10]

Answer:

The correct answer is:

Between 600 and 700 years (B)

Step-by-step explanation:

At a constant decay rate, the half-life of a radioactive substance is the time taken for the substance to decay to half of its original mass. The formula for radioactive exponential decay is given by:

A(t) = A_0 e^{(kt)}\\where:\\A(t) = Amount\ left\ at\ time\ (t) = 75\ grams\\A_0 = initial\ amount = 1000\ grams\\k = decay\ constant\\t = time\ of\ decay = 2500\ years

First, let us calculate the decay constant (k)

75 = 1000 e^{(k2500)}\\dividing\ both\ sides\ by\ 1000\\0.075 = e^{(2500k)}\\taking\ natural\ logarithm\ of\ both\ sides\\In 0.075 = In (e^{2500k})\\In 0.075 = 2500k\\k = \frac{In0.075}{2500}\\ k = \frac{-2.5903}{2500} \\k = - 0.001036

Next, let us calculate the half-life as follows:

\frac{1}{2} A_0 = A_0 e^{(-0.001036t)}\\Dividing\ both\ sides\ by\ A_0\\ \frac{1}{2} = e^{-0.001036t}\\taking\ natural\ logarithm\ of\ both\ sides\\In(0.5) = In (e^{-0.001036t})\\-0.6931 = -0.001036t\\t = \frac{-0.6931}{-0.001036} \\t = 669.02 years\\\therefore t\frac{1}{2}  \approx 669\ years

Therefore the half-life is between 600 and 700 years

5 0
3 years ago
Jocelyn is training for a race by running several miles each day. she tracks her progress by recording her average speed in minu
Luden [163]

Finding the regression equation, her average speed on the 9th day should be expected to be of 6.92 minutes per mile.

<h3>How to find the equation of linear regression using a calculator?</h3>

To find the equation, we need to insert the points (x,y) in the calculator.

Researching the problem on the internet, the values of x and y are given as follows:

  • Values of x: 1, 2, 3, 4, 5, 6.
  • Values of y: 8.2, 8.1, 7.5, 7.8, 7.4, 7.5.

Hence, using a calculator, the equation for the average minutes per mile after t days is given by:

V(t) = -0.15143t + 8.28

Hence, for the 9th day, t = 9, hence the estimate is:

V(9) = -0.15143(9) + 8.28 = 6.92 minutes per mile.

More can be learned about regression equations at brainly.com/question/25987747

#SPJ1

4 0
2 years ago
In Exercises 9 and 10, point B is between A and Con AC. Use the information to
Marizza181 [45]

Answer:n

Step-by-step explanation:

n

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3 years ago
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